English

Is every toric variety an M-variety?

Algebraic Geometry 2007-08-13 v1 Algebraic Topology

Abstract

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.

Keywords

Cite

@article{arxiv.math/0510228,
  title  = {Is every toric variety an M-variety?},
  author = {Frédéric Bihan and Matthias Franz and Clint McCrory and Joost van Hamel},
  journal= {arXiv preprint arXiv:math/0510228},
  year   = {2007}
}

Comments

13 pages

R2 v1 2026-07-22T17:25:46.285Z